Extremal problems in random graphs: Ramsey and Turán type results

Extremal problems in random graphs: Ramsey and Turán type results

von Martin Marciniszyn
Taschenbuch - 9783639414837
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Beschreibung

Revision with unchanged content. The theory of random graphs was founded by Paul Erdos and Alfréd Rényi around 1959. Since then this interesting and fruitful branch of combinatorics attracted many experts from mathematics and theoretical computer science. This book discusses several questions from the realm of classical graph theory in the context of random graphs. In particular, we address so-called Ramsey and Turán type properties of graphs, which are central to the relatively young field of extremal graph theory. Amongst other results, this book establishes an embedding lemma for sparse graphs, which often constitutes the companion to the sparse version of Szemerédi's regularity lemma. A stronger form of this embedding lemma was conjectured by Kohayakawa, Luczak, and Rödl in 1994. This book also continues with the work of Kohayakawa and Kreuter from 1997. We prove strong lower bounds on the edge probability of random graphs that typically allow for an edge coloring without certain monochromatic substructures. Supposing the embedding conjecture of Kohayakawa, Luczak, and Rödl holds, these bounds are tight and give rise to threshold functions.

Details

Verlag AV Akademikerverlag
Ersterscheinung Mai 2012
Maße 220 mm x 150 mm x 8 mm
Gewicht 225 Gramm
Format Taschenbuch
ISBN-13 9783639414837
Auflage Nicht bekannt
Seiten 140

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